Finite Group DatabasebetaFinite Group Databasebeta| order | 5913 |
| isoclinism | isoclinic class of C73⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
| direct product | C27×C73⋊C3 |
| Fitting | C27×C73 ⋊ C3 |
| derived, Sylow | C73 ⋊ C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | C73⋊C3 |
| commutator, hypocenter | C73 | C3×C27 |
| Frattini | C9 | C3×C73⋊C3 |
| Fitting | C27×C73 | C3 |
| socle | C3×C73 | C3×C9 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C27 | |
28 conjugacy classes of subgroups.
729 conjugacy classes — view the full character table.
| maximal subgroup of | C81×C73⋊C3, #31801273, #31801274, … |
| maximal normal subgroup of | C81×C73⋊C3, #31801273, #31801274, … |
| maximal quotient of | C27×#10620321, #31801240, #31801263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5913, 23);